## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

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Side vi

... of a learned gentleman. To which are also added, the Elements of

Spherical Trigonometry, which are commonly taught after the Elements of Euclid.

o - THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. s o I. vi PREFACE.

... of a learned gentleman. To which are also added, the Elements of

**Plane**andSpherical Trigonometry, which are commonly taught after the Elements of Euclid.

o - THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. s o I. vi PREFACE.

Side 197

One part of a straight line cannot be in a

be possible , let AB , part of the straight line ABC , be in the

BC above it : and since the straight line AB is in the

in ...

One part of a straight line cannot be in a

**plane**, and another part above it . * If itbe possible , let AB , part of the straight line ABC , be in the

**plane**, and the partBC above it : and since the straight line AB is in the

**plane**, it can be proс ducedin ...

Side 205

But the

perpendicular to the

be done .

But the

**plane**passing through ED , GH is the**plane**BH ; therefore AF isperpendicular to the

**plane**BH ; therefore , from the given point A , above the**plane**BH , the straight life AF is drawn perpendicular to that**plane**. Which was tobe done .

Side 207

to the

through G draw GH parallel ( 31. 1. ) to ED , and GK parallel to EF , and because

BG is perpendicular to the

to the

**plane**which passes through DE , EF , and let it meet that**plane**in G ; andthrough G draw GH parallel ( 31. 1. ) to ED , and GK parallel to EF , and because

BG is perpendicular to the

**plane**through DE , EF , it shall make right anE gles ... Side 209

For the same reason , because the two parallel

the

is parallel to BD , a side of the triangle ABD , as AE to EB , so is ( 2. 6. ) AX to XD

...

For the same reason , because the two parallel

**planes**GH , KL H A А. are cut bythe

**plane**AXFC , the G common sections AC , XF , are parallel : and because EXis parallel to BD , a side of the triangle ABD , as AE to EB , so is ( 2. 6. ) AX to XD

...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.